Whatever this unit is

Logarithmic Expressions

100

if F(x)=xqn[0,1](x) (the indicator function of the rationals in [0,1]), what is f¹₀ F(x) dx with respect to the Lebesgue measure?"

0

200

Write each logarithmic equation in exponential form

log₉(e^x)=6

9⁶=e^x

300

Rewrite the following exponents as logarithms:

25^3/2 = 125 and 6³ = 216

log₂₅125=3/2 and log₆216=3

400

log₂16 

log₅125

log₁₆4 

log₈1/16

Evaluate the expressions with out a caculator 

x=4

x=3

x=1/2

x=2

500

write each in exponential equation in log from and SOLVE 

e^x+2 =7

4=5^-3x

10^x =x+3

log_e7=x+2 = 1.694

log₅4=-3x= -0.279

log₁₀(x+3)=3 = 0.653

Inverses of Exponetial Functions

100

How do you tell if a data set is exponential, logarithmic, or neither. On a table

Expo-Adding or subtracting on x, multiplying or dividing on y 

Log- Multiplying or dividing on x values adding or subtracting on the y value

200

Are these tables Logarithmic, exponential, or neither

x.       y.                               x.    y.    
1.       5.                              2.    2.   

2.      10.                             4.    3

3       20.                             8.    4

4       40.   16.   5

5       80.   32

1-Exponential

2-Logarithmic

300

x. |-3|-2|0|1|4|6

f(x) 6|3|1|-1|-3|-7

f(f(0))

f^-1(-3)

f^-1(-3)=4

f(f(0))=-1

400

Which Michigan represntative has received the most money through AIPAC

michigans 11th congressional disctrict (Oakland county) Haley Stevens with a total of 5,178,000+ isarel lobby money 

500

what is the inverse of F(x)=2^x

f^-1(x)=log₂(x)

Logarithmic Function Manipulation

100

if F(x)=f^x₀ e^-t2dt, find f''(x) in terms of x and f(x)

DOUBLE JEOPARDY DOUBLE JEOPARDY DOUBLE JEOPARDY DOUBLE JEOPARDY DOUBLE JEOPARDY DOUBLE JEOPARDY DOUBLE JEOPARDY 

f''(x)=-2xe^-x(-x)=-2xf'(x)?

200

Condense this expression into a single logarithm

5log₃x - 7log₃y + log₃z

Log₃(x⁵z/y⁷)

300

 solve logarithmic equations 

log₄(3x-5)=3

3+4in(2x)=15 

x=23

x=e³/2

400

6(10)^2x=48

log then solve chat 

500

3(log 6x - log .5y) - 7(log 2 + 3log 4)

log (6x/33y)^3

Math

100

A rocket has an initial mass of 2000 kg (including fuel) and a final mass of 1000 kg after burning fuel. If the exhaust velocity is 3000 m/s3000, what is the rocket’s final velocity?"

2079 M/s

200

log -2 = x

x = undefined

300

square root of (2-3!)

2i

400

Where does Henry Westfall want to find his future wife

rural china

500

"Let G be a group of order 15. What is the number of elements of order 5 in G?"

Hint 

Lagrange’s Theorem: the order of an element divides the order of the group.

4

Logarithmic Expressions cont

100

Convert 6³=12

log₆12=3

200

3^4x+1-5=22

x=0.5

300

log₄₉x=-1/2

0.1429

400

What did Mrs. Proctor say her favorite Anime was

Fruit basket

500

2^3x-2 <4^x

x < 2